| 課程名稱 Course Title |
(中文) 隨機過程 (英文) Random Variable & Stochastic Process |
開課單位 Departments |
電機工程學系 | ||
| 課程代碼 Course No. |
E4070 | ||||
| 授課教師 Instructor |
龔宗鈞 | ||||
| 學分數 Credit |
3.0 | 必/選修 core required/optional |
選修 | 開課年級 Level |
大四 |
| 先修科目或先備能力Course Pre-requisites：工程數學(微積分、矩陣、富氏分析) | |||||
| 課程概述與目標 Course Overview and Goals：使學生了解隨機變數與隨機過程之數學理論與物理觀念，並能夠應用於系統上之分析與設計。 | |||||
| 教科書 Textbook |
作者 : Peyton Z. Peebles, Jr. 書名 : Probability, Random Variables and Random Signal Principles 出版社 : McGraw Hill(ISBN 0-07-118181-4) |
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| 參考教材 Reference |
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| 課程大綱 Syllabus |
學生學習目標 Learning Objectives |
單元學習活動 Learning Activities |
學習成效評量 Evaluation |
備註 Notes |
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| 週 Week | 單元主題 Unit topic |
內容綱要 Content summary |
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| 1 | Probability | 1. Probability Introduced Through Sets and Relative Frequency 2. Joint and Conditional Probability |
To understand: experiments and sample spaces, discrete and continuous sample spaces, events, probability definition and axioms, joint and conditional probability, Bayes' theorem. |
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| 2 | Probability | 1. Independent Events 2. Combined Experiments 3. Bernoulli Trials |
To understand: two events, multiple events, properties of independent events, combined sample space, events on the combined sample space, Bernoulli trials. |
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| 3 | The Random Variable | 1. The Random Variable Concept 2. Distribution Function 3. Density Function |
To understand: definition of random variable, conditions for a function to be a random variable, discrete and continuous random variable, mixed random variable, distribution function, density function. |
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| 4 | The Random Variable | 1. The Gaussian Random Variable 2. Other Distribution and Density Examples 3. Conditional Distribution and Density Function |
To understand: the Gaussian random variable, binomial distribution, Possion distribution, uniform distribution, conditional distribution, conditional density function. |
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| 5 | Operations on One Random Variable (RV) | 1. Expection 2. Moments |
To understand: expected value of a RV, expected value of a function of a RV, moments about the origin, central moments, variance and skew, Chebychev's inequality. |
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| 6 | Operations on One Random Variable (RV) | 1. Transformations of a Random Variable | To understand: monotonic transformations of a continuous RV, nonmonotonic transformations of a continuous RV, transformation of a discrete RV. |
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| 7 | Multiple Random Variables | 1. Vector Random Variables 2. Joint Distribution and Its Properties |
To understand: joint distribution function and its properties, marginal distribution functions. |
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| 8 | Multiple Random Variables | 1. Joint Density and Its Properties 2. Conditional Distribution and Density |
To understand: joint density function and its properties, marginal density functions, conditional distribution and density. |
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| 9 | Random Variables | 1. Probability 2. Random Variables 3. Operations on One Random Variable 4. Multiple Random Variables |
To understand: 1. Probability 2. Random Variables 3. Operations on One Random Variable 4. Multiple Random Variables |
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| 10 | Multiple Random Variables | 1. Statistical Independence 2. Distribution and Density of a Sum of RVs 3. Central Limit Theorem |
To understand: statistical independence of RVs, distribution and density of a sum sum of two RVs, central limit theorem. |
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| 11 | Operations on Multiple Random Variables | 1. Expected Value of a Function of Random Variables 2. Joint Characteristic Functions 3. Joint Gaussian Random Variables |
To understand: joint moments about the origin, joint characteristic functions, joint Gaussian RVs. |
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| 12 | Operations on Multiple Random Variables | 1. Transformations of Multiple Random Variables 2. Sampling and Some Limit Theorems |
To understand: transformations of multiple RVs, sampling and some limit theorems. |
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| 13 | Random Processes-Temporal Characteristics | 1. The Random Process Concept 2. Stationarity and Independence |
To understand: classification of processes, statistical independence, first-order stationary process, second-order and wide-sense stationarity, N-order and strict-sense stationarity, time average and ergodicity. |
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| 14 | Random Processes-Temporal Characteristics | 1. Correlation Functions 2. Gaussian Random Processes |
To understand: autocorrelation function and its properties, cross-correlation function and its properties, covariance functions. |
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| 15 | Random Processes-Spectral Characteristics | 1. Power Density Spectrum and Its Properties 2. Relationship between Power Spectrum and Autocorrelation Function 3. Cross-Power Density Spectrum and Its Properties |
To understand: the power density spectrum and its properties, bandwidth of the power density spectrum, relationship between power spectrum and autocorrelation function, the cross-power density spectrum and its properties. |
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| 16 | Random Processes-Spectral Characteristics | 1. Power Spectrum for Discrete-Time Processes and Sequences 2. Some Noise Definitions |
To understand: discrete-time processes, discrete-time sequences, white noise and colored noise. |
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| 17 | Linear Systems with Random Inputs | 1. Linear System Fundamentals 2. Random Signal Response of Linear System 3. Spectral Characteristics of System Response |
To understand: mean and mean-squared value of system response, autocorrelation function of response, cross-correlation functions of input and output, power density spectrums of response, cross-power density spectrums of input and output. |
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| 18 | Random Processes-Spectral Characteristics | 1. Random Processes-Temporal Characteristics 2. Random Processes-Spectral Characteristics 3. Linear Systems with Random Inputs |
To undserstand: random processes-temporal characteristics, random processes-spectral characteristics, linear systems with random inputs. |
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教學要點概述 Overview of Teaching Points： |